Abstract
We study the intersection of an algebraic variety with the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves. For this intersection we show a Manin- Mumford type statement. This answers some questions posed by Corvaja-Masser-Zannier which arose in connection with their investigation of the intersection of an algebraic curve with the maximal compact subgroup of various algebraic groups. In particular they proved that these intersections are finite for universal vectorial extensions of elliptic curves. Using Khovanskii’s zero-estimates combined with a stratification result of Gabrielov-Vorobjov and recent work of the authors, we obtain effective bounds for this intersection that only depend on the degree of the algebraic variety and the dimension of the group. As a corollary, we obtain new uniform results of Manin-Mumford type for additive extensions of certain abelian varieties.
Original language | English |
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Article number | rnz207 |
Journal | International Mathematics Research Notices |
Volume | 0 |
Early online date | 20 Nov 2019 |
DOIs | |
Publication status | Published - 20 Nov 2019 |